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Some weighted norm inequalities for a one-sided version of $g*_{λ}$

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de Rosa L., Segovia C.

Studia Mathematica

2006

tom 176

nr 1

21-36

We study the boundedness of the one-sided operator $g⁺_{λ,φ}$ between the weighted spaces $L^{p}(M¯w)$ and $L^{p}(w)$ for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of $g⁺_{λ,φ}$. For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of $g⁺_{λ,φ}$ from $L^{p}((M¯)^{[p/2]+1} w)$ to $L^{p}(w)$, where $(M¯)^{k}$ denotes the operator M¯ iterated k times.

Ograniczanie wyników

1 Studia Mathematica

1 Segovia C.

1 de Rosa L.

1 2006

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Some weighted norm inequalities for a one-sided version of $g*_{λ}$